Remember, the company's reason for offering you severance is usually to avoid lawsuits or reputational damage. Even though you're losing your job, you may still have leverage to obtain a better deal.
A better deal doesn't have to involve cash. Healthcare is expensive, and some companies will help subsidize the continuation of your employer-provided health insurance premium via COBRA for a certain period to make sure you keep your insurance. Your companies may also offer outplacement services, designed to help you find another job. If you have an employer-issued laptop or phone, you could also negotiate with your former employer to keep them.
If possible, find out how competitors handle severance. If it's a better deal, ask your former employer to match it. If your former employer wants your help with the transition, use that as leverage, as well.
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